Implicit elliptic boundary-value problems with discontinuous nonlinearities

✍ Scribed by Marano, Salvatore A.

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 818 KB
• Volume: 4
• Category: Article
• ISSN: 0927-6947
• DOI: 10.1007/bf00419370

✦ Synopsis

Let R be a bounded domain in W" (n > 3) having a smooth boundary, let cp be an essentially bounded real-valued function defined on R x We, and let 1c, be a continuous realvalued function defined on a given subset Y of We. In this paper, the existence of strong solutions u E W'J'(R,EX~) n W,:Pp(R,~h) (n/2 < p < +oo) to the implicit elliptic equation $(-Au) = cp(z,u), with u = (ul, u2,. . . , uh) and Au = (Au,, Au2,. . , Auh), is established. The abstract framework where the problem is placed is that of set-valued analysis.